The posterior density for ordinal and binary models do not have a tractable
density and so the parameters cannot be sampled directly. While the
Metropolis-Hastings (MH) algorithm [1]}, [2]} can be employed to sample the parameters, the standard and
more convenient approach is to consider data augmentation
[3]}. In this approach, the joint posterior density is
augmented by a latent variable \(z\)  and the augmented joint posterior
\(\pi (\theta ,z|y)\)  is written as,
\(\pi (\theta ,z|y) \propto \pi (\theta ) f(z,y|\theta ) =\pi (\theta ) f(z|\theta ) f(y|z,\theta ).\) 
